Measurement of the Velocity Gradient Tensor in Turbulent Flows

Wallace, J. M.; Vukoslavčević, Petar

doi:10.1146/annurev-fluid-121108-145445

Cited by 72 publications

(34 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The power law exponents d n are connected with the exponents of the longitudinal velocity increment moments in the inertial range, ðΔ r v x Þ n ∝ r ζ n . Definition [4] shows that the determination of the full dissipation field requires the measurement of all nine components of the velocity gradient tensor ∂v i /∂x j , which is still a challenging experimental task (31). Numerical simulations also become very demanding because high-amplitude events of the energy dissipation field have to be resolved correctly (9).…”

Section: Universal Scaling and Transition To Intermittencymentioning

confidence: 99%

Small-scale universality in fluid turbulence

Schumacher

Scheel

Krasnov

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

113

View full text Add to dashboard Cite

Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i) at Reynolds numbers Re ∼ 10 2 the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully developed high Reynolds number turbulence, and (ii) beyond the transition point, the statistics of the rate of energy dissipation in all three flows obey the same Reynolds number power laws derived for homogeneous turbulence. These results allow us to claim universality of small scales even at low Reynolds numbers. Our results shed new light on the notion of when the turbulence is fully developed at the small scales without relying on the existence of an extended inertial range.fluid dynamics | energy dissipation rate A n enduring notion in the phenomenology of turbulence is the universality of small scales. It has been taken for granted in theoretical approaches (e.g., refs.

show abstract

Section: Universal Scaling and Transition To Intermittencymentioning

confidence: 99%

Small-scale universality in fluid turbulence

Schumacher

Scheel

Krasnov

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

113

View full text Add to dashboard Cite

show abstract

“…Achieving this spatial resolution in an experiment is highly nontrivial. Multisensor hot-wire probes (Wallace & Vukoslavcević 2010) can provide the required resolution, but acquire only single-point Eulerian information and typically require the use of Taylor's hypothesis and a strong mean velocity. Nonintrusive optical methods, such as laser-induced fluorescence (LIF), particle image velocimetry (PIV), and particle tracking are potentially viable alternatives.…”

Section: Introductionmentioning

confidence: 99%

Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

Kramel

Ouellette

et al. 2015

J. Fluid Mech.

View full text Add to dashboard Cite

We present simultaneous experimental measurements of the dynamics of anisotropic particles transported by a turbulent flow and the velocity gradient tensor of the flow surrounding them. We track both rod-shaped particles and small spherical flow tracers using stereoscopic particle tracking. By using scanned illumination, we are able to obtain a high enough seeding density of tracers to measure the full velocity gradient tensor near the rod. The alignment of rods with the vorticity and the eigenvectors of the strain rate show agreement with numerical simulations. A full description of the tumbling of rods in turbulence requires specifying a seven-dimensional joint probability density function (PDF) of five scalars characterizing the velocity gradient tensor and two scalars describing the relative orientation of the rod. If these seven parameters are known, then Jeffery's equation specifies the rod tumbling rate and any statistic of rod rotations can be obtained as a weighted average over the joint PDF. To look for a lower-dimensional projection to simplify the problem, we explore conditional averages of the mean-squared tumbling rate. The conditional dependence of the mean-squared tumbling rate on the magnitude of both the vorticity and the strain rate is strong, as expected, and similar. There is also a strong dependence on the orientation between the rod and the vorticity, since a rod aligned with the vorticity vector tumbles due to strain but not vorticity. When conditioned on the alignment of the rod with the eigenvectors of the strain rate, the largest tumbling rate is obtained when the rod is oriented at a certain angle to the eigenvector that corresponds to the smallest eigenvalue, because this particular orientation maximizes the contribution from both the vorticity and strain.

show abstract

“…Prior numerical and experimental studies (see e.g. Sreenivasan & Antonia 1997;Ishihara, Gotoh & Kaneda 2009;Wallace & Vukoslavcević 2010) have shown, however, that ε is highly intermittent, resulting in local values of ε that can be orders of magnitude larger than the mean, even for turbulent flows at moderate Reynolds numbers. Such high amplitudes are, by definition, the result of very large velocity gradients, or tiny shear layers across which the velocity varies significantly.…”

Section: Introductionmentioning

confidence: 99%

Local dissipation scales and energy dissipation-rate moments in channel flow

et al. 2012

View full text Add to dashboard Cite

Local dissipation-scale distributions and high-order statistics of the energy dissipation rate are examined in turbulent channel flow using very high-resolution direct numerical simulations at Reynolds numbers Re τ = 180, 381 and 590. For sufficiently large Re τ , the dissipation-scale distributions and energy dissipation moments in the channel bulk flow agree with those in homogeneous isotropic turbulence, including only a weak Reynolds-number dependence of both the finest and largest scales. Systematic, but Re τ -independent, variations in the distributions and moments arise as the wall is approached for y + 100. In the range 100 < y + < 200, there are substantial differences in the moments between the lowest and the two larger values of Re τ . This is most likely caused by coherent vortices from the near-wall region, which fill the whole channel for low Re τ .

show abstract

Measurement of the Velocity Gradient Tensor in Turbulent Flows

Cited by 72 publications

References 61 publications

Small-scale universality in fluid turbulence

Small-scale universality in fluid turbulence

Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

Local dissipation scales and energy dissipation-rate moments in channel flow

Contact Info

Product

Resources

About